Why did you pick 1 for x value specifically? (where 2x=0)
It really works for any value of x. But field charachteristics are defined for 1. Because if 1 + 1 = 0 then it is true for any element. That is why we resrict out attention to 1.
Don't worry about it ...it just takes me longer to get it but i'll get it.
1 is the unity element. otherwise, we have 2x = 0 for all x in R, so either definition is satisfied. I was just trying to show you why considering 1 was relevant